Study of Interfacial Tension Between an Organic Solvent and Aqueous Electrolyte Solutions Using Electrostatic Dissipative Particle Dynamics Simulations

1 Study of Interfacial Tension between an Organic Solvent and Aqueous Electrolyte Solutions Using Electrostatic Dissipative Particle Dynamics Simulations. E. Mayoral (1), E. Nahmad-Achar(2) 1 Instituto Nacional de Investigaciones Nucleares, Carretera México-Toluca s/n, La Marquesa Ocoyoacac, Estado de México CP 52750, México. Email address: [email protected] 2 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México (UNAM), Apartado Postal 70-543, 04510 México D.F. Email address: [email protected] ABSTRACT The study of the modification of interfacial properties between an organic solvent and aqueous electrolyte solutions is presented by using electrostatic Dissipative Particle Dynamics (DPD) simulations. In this article the parametrization for the DPD repulsive parameters aij for the electrolyte components is calculated considering the dependence of the Flory-Huggins χ parameter on the concentration and the kind of electrolyte added, by means of the activity coefficients. In turn, experimental data was used to obtain the activity coefficients of the electrolytes as a function of their concentration in order to estimate the χ parameters and then the aij coefficients. We validate this parametrization through the study of the interfacial tension in a mixture of n-dodecane and water, varying the concentration of different inorganic salts (NaCl, KBr, Na2SO4 and UO2Cl2). The case of HCl in the mixture n-dodecane/water was also analyzed and the results presented. Our simulations reproduce the experimental data in good agreement with previous work, showing that the use of activity coefficients to obtain the repulsive DPD parameters aij as a function of concentration is a good alternative for these kinds of systems. I. INTRODUCTION The change of interfacial tension by the use of additives has an important effect for many industrial applications which involve oil/water interfaces [1]. The performance of this kind of additives is in strong correlation with the characteristics of the medium. In particular the ionic strength, pH, temperature and pressure play an important role in the behavior of these complex systems. Understanding how these conditions modify the interfacial tension is a fundamental task in order to design formulations ad hoc for particular systems. Various experimental data and theoretical models for the calculation of interfacial tension between an organic solvent and aqueous electrolyte solutions have been presented. Aveyard and Saleem [2] reported the surface tensions of different aqueous electrolytes solutions and their interfacial tensions with n-dodecane. They discussed their results in terms of both electrostatic theory and dispersion force theory of interfaces, and presented an expression considering a salt free layer, taking into account the non-ideality of the solution. Desnoyer et al. [3] proposed a model by combining thermodynamical equations with an adsorption model. The interfacial tension was obtained from the isothermal Gibbs equation and the variation of interfacial tension as a function of concentration was modeled using a Langmuir-type adsorption equation. The results obtained present a reasonable correspondence with the experimental data. Li and Lu [4, 5] introduced a prediction model for the 2 calculation of the interfacial tension between an organic solvent and aqueous multielectrolyte solutions. In this model, the activity coefficients for the electrolytes are calculated using the Meissner method [6]. Their results were successfully applied to the prediction of interfacial tensions reported in the literature. Experimental study of these and more complex systems with electrolytic multi-components is complicated, and requires the design, development and testing of the systems at many different conditions, making this study expensive and limited. To avoid this kind of limitations, numerical simulation offers a viable alternative to help in the study and design of formulations with different components, which could give a better performance even under extreme conditions impossible to handle in the laboratory. Recently, mesoscopic simulation has shown to be an attractive research area for both the academic and industrial communities. Complex industrial formulations have to deal with systems composed of large amounts of various kinds of molecules, interacting at different length and time scales, and in these cases using a coarse grained approximation is recommendable. Along these lines, Onuki [7] examined the ion distributions (at low ion densities) around an air-salty water interface in the scheme of the Ginzburg-Landau theory, accounting for electrostatic, solvation effects, and image forces, deriving a number of general functional relations for the dielectric constant of the medium, the image interaction, solvation effects and wetting transitions. In [8] he extended this work for less polar fluids and derived a general expression for the surface tension of electrolyte systems, which contains a negative electrostatic contribution proportional to the square root of the bulk salt density. The excess liquid-liquid interfacial tension between two electrolyte solutions as a function of the ionic strength was studied by Bier et al. [9], finding different regimes dependent on unequal ion partitioning and charge separation. By using a coarse-grained simulation method for complex charged systems, coupling a hydrodynamic description to a free energy functional accounting for the interactions between solvent(s) and charged solutes, Rotenberg et al. [10] studied the transport of charged tracers in charged porous media, the deformation of an oil droplet in water under the effect of an applied electric ﬁeld, and the distribution of ions at an oil– water interface as a function of their affinity for both solvents. One of the most important mesoscopic simulation approaches is via dissipative particle dynamics (DPD), introduced some years ago by Hoogerbruge and Koelman [11], who proposed to simulate these complex systems by soft spherical beads interacting through a simple pair-wise potential and thermally equilibrated through hydrodynamics. In this formalism, the beads follow Newton´s equations of motion, involving a repulsive parameter aij in the conservative part of the force. Therefore, the consistency of the results depends strongly on how the essential molecule’s characteristics are included into the interaction parameters aij between the DPD beads. Later, Groot and Warren established a functional relationship between the conservative repulsion DPD parameters aij and the Flory-Huggins χ-parameter theory (FH) [12], using the solubility parameters to estimate the cross parameters corresponding with different species. The magnitude of the like- like bead interactions (aii) was related with the isothermal compressibility of the medium at standard conditions. An improved method of parametrization was introduced by Travis et al. [13]. In this, they take advantage of the connection between DPD and the Scatchard-Hildebrand regular solution theory [14, 15], eliminating the limitation of identical repulsive interactions between equal beads, and they link every conservative interaction among beads directly to cohesive energy densities. They presented an alternative method for obtaining the self-interaction parameters and 3 also an alternative to calculating the cross interaction parameter using the cohesive energy densities of the pure fluid. Electrostatic interactions were introduced into DPD by Groot [16] and by González-Melchor et al. [17]. In both cases the point charge at the center of the DPD particle is replaced by a charge distribution over the particle. Groot solves the problem by calculating the electrostatic field on a grid, and González-Melchor and one of us solve the problem adapting the standard Ewald method to DPD particles. In complex electrostatic systems, the conservative force is composed of the electrostatic contribution apart from the DPD repulsive parameter aij. As is natural to expect, these two contributions are in strong relation with the concentration of charged particles in the system. A study of the interface between aqueous electrolytes and air has been done by Ghoufi and Malfreyt [18, 19], showing that the surface tension of NaCl and NaF solutions can be predicted from electrostatic many-body DPD simulations (MDPD). As MDPD is composed of an attractive term and a density dependent repulsive term, the authors developed a multi-scale method to obtain these parameters from atomistic simulations using Flory-Huggins theory. In this work, we present an alternative methodology to simulate the interfaces between two immiscible liquids (salt solutions and an organic liquid) by using the standard electrostatic DPD simulations, where we only have a repulsive parameter in contrast with the MDPD used by Ghoufi and Malfreyt. To appropriately include the electrostatic information, and in order to obtain realistic parameters, we take into account the concentration of the ions. With this in mind, we introduce a parametrization which considers the dependence of the Flory-Huggins χ parameters on the electrolyte concentration by using of the Hildebrand –Scatchard regular solution theory via the activity coefficients [14, 15, 20]. The activity coefficients are taken from reported experimental data [21]. The dependence of the aij parameters with the ion concentration is then considered through the χ parameter in the DPD simulation. As will be explained later, it arises from the

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